Near interaction preconditioner using overlapped localizing local global solution modes

Multilevel fast multipole algorithm (MLFMA) has been widely used to expedite the iterative solution of the linear systems that arise from discretizing integral equations for electromagnetic applications. However, the slow convergence rate, or non-convergence, of the iterative solver must be improved by either changing the underlying formulation or by using a good preconditioner. In this paper, we form an approximate inverse of the near interaction part of the system matrix and used it as a preconditioner to improve the convergence of an MLFMA based iterative solvers. The near interaction matrix is defined and filled by an existing MLFMA code, and it is factored and inverted using overlapped localizing local global solution modes (OL-LOGOS). Numerical results shows that the OL-LOGOS factored near interaction preconditioner is effective in improving the convergence rate.